• 한국인지과학회:학술대회논문집
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• 한국인지과학회 2000년도 춘계 학술대회
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• pp.322-328
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• 2000

This study discusses cognition as a computable mapping in cognitive system and relates G del's Incompleteness Theorems to the computability of cognition from a metamathematical perspective. Understanding cognition as a from of computation requires not only Turing machine models but also neural network models. In previous studies of computation by cognitive systems, it is remarkable to note how little serious attention has been given to the issue of computation by neural networks with respect to G del's Incompleteness Theorems. To address this problem, first, we introduce a definition of cognition and cognitive science. Second, we deal with G del's view of computability, incompleteness and speed-up theorems, and then we interpret G del's disjunction on the mind and the machine. Third, we discuss cognition as a Turing computable function and its relation to G del's incompleteness. Finally, we investigate cognition as a neural computable function and its relation to G del's incompleteness. The results show that a second-order representing system can be implemented by a finite recurrent neural network. Hence one cannot prove the consistency of such neural networks in terms of first-order theories. Neural computability, theoretically, is beyond the computational incompleteness of Turing machines. If cognition is a neural computable function, then G del's incompleteness result does not limit the compytational capability of cognition in humans or in artifacts.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1998년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Spring 1998
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• pp.413-420
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• 1998

In this paper, two methods, Stepp's and EQHAZARD, are introduced and applied to a recent earthquake catalog for the entire Korean Peninsula that can estimate the seismicity by incorporating the incompleteness of the earthquake catalog. EQHAZARD method, different from Stepp's method in that it used priori information besides the assumption of stationary Poisson process of the earthquakes, produces the higher seismicity rate for the smaller earthquakes. EQHAZARD method are also used to estimated the incompleteness of the recent earthquake catalog for the southern part of the Korean Peninsula in terms of the Probability of Activity for the specified earthquke magnitude classes and time periods. It is believed that the Probability of Activity thus obtained can be used as a strong priori information in estimating the seismicity for a seismic source within the region where there are not enough earthquakes detected. Finally, it is demonstrated that the arbitrary selection of the methods. of incompleteness analysis brings quite different seismic hazard results, which suggests the need to employ a rigid quantitative method for incompleteness analysis in estimating the seismicity parameters in order to reduce the uncertainty in the Seismic Hazard Results with the EQHAZARD method being one of the competent practical alternatives.

• 한국수학사학회지
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• 제15권3호
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• pp.75-82
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• 2002

G$\ddot{o}$del's metamathematical program from Incompleteness to Speed-up theorems shows the necessity of ever higher systems beyond the fixed formal system and devises the relative consistency.

• 한국정보과학회 언어공학연구회:학술대회논문집(한글 및 한국어 정보처리)
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• 한국정보과학회언어공학연구회 1995년도 제7회 한글 및 한국어 정보처리 학술대회
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• pp.258-263
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• 1995

마음과 기계의 관계에 대한 $G{\ddot{o}}del's$의 선언결론(disjunctive conclusion)은 마음과 정보처리형식체계의 논리적 동치성을 함의하고 있다. 그리고 $G{\ddot{o}}del's$의 불완전성 정리(Incompleteness Theorems)에 따르면 마음과 정보처리형식체계의 논리적 동치성은 무모순이며, 동치성 반증의 이론은 그 모델을 가질 수 없다.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.555-563
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• 2004

In classification and discrimination, we often face with incomplete group variable arising typically from many missing values and/or incredible cases. This paper suggests the use of K-means clustering for pre-adjusting incompleteness and in turn classification based on generalized statistical distance is performed. For illustrating the proposed procedure, simulation study is conducted comparatively with CART in data mining and traditional techniques which are ignoring incompleteness of group variable. Simulation study manifests that our methodology out-performs.

• 한국수학사학회지
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• 제19권2호
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• pp.47-58
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• 2006

본 논문에서는 괴델의 삶과 업적을 소개하고, 그의 불완전성정리의 함의하는 바가 인식론적이고 윤리적인 의미를 가지는 여백을 확보하는데 있다는 것을 주장한다. 그리고 그 함의가 '여백의 철학'을 지지함을 논의한다.

• 한국전자통신학회논문지
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• 제19권1호
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• pp.295-300
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• 2024

본 논문에서는 SNOMED CT 용어체계가 가지는 불완전성을 논의하고 이를 유지하는 방법으로 형제 노드 간 유사성을 평가하는 지표를 제안한다. SNOMED CT는 방대한 양의 의학용어를 포함하고 있으나 계층구조 내 컨셉의 누락 등 온톨로지의 불완전성 문제가 존재한다. 누락된 컨셉 발견을 위해 다수의 노드로 구성된 형제 노드 그룹 내에서의 노드 간 유사도 평가를 위한 지표를 제안하고 유사도가 낮은 그룹을 도출하였다. 2023년 3월 SNOMED CT 국제 배포판에 적용하여 형제 노드 그룹들의 유사도를 분석한 결과 임상적 발견 컨셉의 하위 컨셉들 중 2개 이상의 형제 노드를 가진 29,199개의 형제 노드 그룹의 평균 유사도는 0.81로 나타났다. 반면, 유사도가 가장 낮은 그룹은 중독 컨셉의 자식 컨셉으로 그 유사도는 0.0036으로 확인되었다.

• 한국소음진동공학회논문집
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• 제12권4호
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• pp.302-309
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• 2002

A FRF-based substructuring method attempts to predict the dynamic characteristics of a complex structure from predetermined FRFs of the comprising uncoupled substructures. Although this method has the advantage of being able to incorporate experimental component FRFs directly, it is prone to errors : measurement errors, coordinate incompleteness, modal incompleteness, etc. Among the various sources of errors, this paper deals with the problem of modal incompleteness (or residual problem) of which importance is underestimated compared to others. It is a well-known rule of thumb that such a problem can be overcome by including modes up to 2 or 3 times the upper frequency of interest. Using a simulated case study, it is demonstrated that even including modes up to 20 times the upper frequency of interest does not guarantee a satisfactory result. A method to compensate the residual errors is introduced. This method requires the whole FRF matrices of substructures which is practically impossible for a complex structure. An applicable alternative is suggested and applied successfully to the case study. Finally, the effects of measurement errors on the residual compensation are also discussed.

• 한국수학사학회지
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• 제13권1호
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• pp.137-141
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• 2000

This paper discusses Godel's Disjunctive Conclusion in terms of cognitive science and his Incompleteness Theorems from a metamathematical perspective.

• 한국수학사학회지
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• 제29권1호
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• pp.31-44
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• 2016

This essay aims to suggest roughly the "philosophy of limits." The limits mainly refer to those of human experiences and rational thoughts. The philosophy of limits consist of three theses and two consequences(L, M). (1) The limits are necessarily supervenient in the course of searching knowledge. (2) The limits cannot be dissipated ultimately. (3) To recognize the limits is not only an intellectual recognition but also a beginning of whole personality's reaction. (L) It is a rational decision to accept the limits and leave the margins (yeoback/yeoheuck) rather than to try to remove them. (M) To leave the margins (yeoback/yeoheuck) is characteristic of being human, and enables one to harmoniously communicate with others. To justify the philosophy of limits, this essay examine the limits discussed in mathematics and philosophy: set theory, Godel's Incompleteness Theorem, Galois Theorem in mathematics; and Hume, Kant, Kierkegaard, and Wittgenstein in philosophy. I try to interpret consciousness of limits in various cultures. I claim that consciousness of the limits contribute to lucidity of human identity, communication between persons, stimulation of creative thinking.